Add sum_to_zero transform

[WardBrian]

Draft because it relies on stan-dev/stan#3308 and one of stan-dev/math#3099 stan-dev/math#3101

Submission Checklist

• Run unit tests
• Documentation
  • If a user-facing facing change was made, the documentation PR is here: TBD

Release notes

Added the sum_to_zero transform for vector types.

Copyright and Licensing

By submitting this pull request, the copyright holder is agreeing to
license the submitted work under the BSD 3-clause license (https://opensource.org/licenses/BSD-3-Clause)

[codecov]

Codecov Report

Attention: Patch coverage is 42.85714% with 8 lines in your changes missing coverage. Please review.

Project coverage is 89.49%. Comparing base (0ea83bb) to head (13938a8).

Files	Patch %	Lines
src/frontend/Pretty_printing.ml	25.00%	3 Missing ⚠️
src/analysis_and_optimization/Mir_utils.ml	0.00%	2 Missing ⚠️
src/frontend/Ast_to_Mir.ml	60.00%	2 Missing ⚠️
src/middle/Transformation.ml	0.00%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1443      +/-   ##
==========================================
- Coverage   89.52%   89.49%   -0.03%     
==========================================
  Files          63       63              
  Lines       10614    10618       +4     
==========================================
+ Hits         9502     9503       +1     
- Misses       1112     1115       +3     

Files	Coverage Δ
src/frontend/Typechecker.ml	91.78% <100.00%> (+<0.01%)	⬆️
src/stan_math_backend/Lower_expr.ml	93.55% <100.00%> (+0.01%)	⬆️
src/middle/Transformation.ml	87.50% <0.00%> (-3.81%)	⬇️
src/analysis_and_optimization/Mir_utils.ml	76.05% <0.00%> (-0.36%)	⬇️
src/frontend/Ast_to_Mir.ml	94.15% <60.00%> (-0.20%)	⬇️
src/frontend/Pretty_printing.ml	92.28% <25.00%> (+0.02%)	⬆️

[nhuurre]

The original issue asks for zero_sum_vector but here it has been renamed to sum_to_zero. I didn't see any discussion as to why. Personally, I prefer zero_sum (without _vector, cf. ordered)

[WardBrian]

@bob-carpenter listed these for consideration in an email with me before implementation work began

• zero_sum
• zero_sum_vector
• sum_to_zero
• sum_to_zero_vector

I don't have that strong of a preference, but I do think sum_to_zero is more self explanatory without being that much longer

[bob-carpenter]

I like sum_to_zero_vector, because that's how I'd say it out loud.

[WardBrian]

sum_to_zero_vector is shorter than some of the other types (I think cholesky_factor_corr holds that title?), so if that sounds better to others I'm happy to make the change

[SteveBronder]

Good!